Application of the Method of Straight Lines for Solving Parabolic Equations with Arbitrary Linear Boundary Conditions
Main Article Content
Abstract
A method for applying the straight-line technique by transforming a problem with arbitrary linear boundary conditions into a Dirichlet problem is developed. Assuming the boundary values of the desired function are given, the Dirichlet problem is solved. The actual boundary values of the desired functions are found by aligning the assumed boundary values with the newly obtained values according to boundary condition approximations. These values are then used to implement the straight-line method, ensuring second-order accuracy for equation and boundary condition approximations.
Article Details
Issue
Section
How to Cite
References
Zhiwei Chong, “A qualitative analysis to simple harmonic motion,” arXiv preprint arXiv:2209.12662 (2022). ( Accepted by The Physics Teacher)
The subscript in ????????stands for physical, while that in ????????actually stands for the center of percussion.
Hugh G. Gauch, Scientific Method in Practice, (Cambridge University Press, Cambridge, 2003) p. 269.
P. N. Raychowdhury, and J. N. Boyd, “Center of percussion,” Am. J. Phys. 47(12):1088-1089 (1979).
J. Hass, C. Heil, and M. D. Weir, Thomas’ Calculus, 14th ed. (Pearson Education, Boston, 2018), p. 191.
Фаддеева В.Н. Метод прямых в применении к некоторым краевым задачам. - Тр. МИ АН СССР, 1949, том 28. - С. 73-103. (Из Общероссийского математического портала Math-Net).
Каримбердиева С. Численные методы решения дифференциально-разностных уравнений в параллелепипеде, шаре и цилиндре. - Ташкент: Фан, 1983. - 112 с.
Хужаев И.К., Хужаев Ж.И., Равшанов З.Н. Аналитическое решение задачи о собственных значениях и векторах матрицы перехода из параболического уравнения к конечноразностным уравнениям при решении задачи Дирихле // Узбекский журнал информатики и энергетики, 2017, №2. - С. 12-19.